A363323 Total number of parts coprime to n in the partitions of n into 5 parts.

0, 0, 0, 0, 5, 4, 10, 10, 22, 19, 50, 28, 90, 63, 102, 104, 235, 108, 350, 192, 343, 313, 705, 301, 831, 576, 919, 684, 1665, 515, 2135, 1274, 1813, 1555, 2540, 1324, 4155, 2360, 3397, 2359, 6130, 1953, 7345, 3858, 4925, 4854, 10310, 3890, 10790, 5457, 9421, 7351, 16330, 6077

Offset

1,5

Links

Table of n, a(n) for n=1..54.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-l)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} (c(i) + c(j) + c(k) + c(l) + c(n-i-j-k-l)), where c(x) = [gcd(n,x) = 1] and [ ] is the Iverson bracket.

Example

The partitions of 9 into 5 parts are: 1+1+1+1+5, 1+1+1+2+4, 1+1+1+3+3, 1+1+2+2+3, and 1+2+2+2+2. 9 is relatively prime to 1, 2, 4 and 5. Since there are 22 total parts in these partitions that are coprime to 9, a(9) = 22.

Crossrefs

For similar sequences into k parts for k = 2..10, see: A000010(n>2) (k=2), A363278 (k=3), A363322 (k=4), this sequence (k=5), A363324 (k=6), A363325 (k=7), A363326 (k=8), A363327 (k=9), A363328 (k=10).

Sequence in context: A152064 A088482 A163888 * A309545 A285105 A360682

Adjacent sequences: A363320 A363321 A363322 * A363324 A363325 A363326

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 27 2023

Status

approved